On Monday night, an Irish friend long resident in London sent an email to me in Dublin. He'd noticed that Buckingham Palace had tweeted a welcome to the Irish president Michael D Higgins on the occasion of the beginning of the first state visit of an Irish head of state to Britain. What was remarkable was that the tweet was written in the Irish language, Gaelic. "I've seen everything now," my friend said.

Language is important. Nuance conveys respect. The Queen's visit to Ireland in 2011 was an immense success, in no small part because of the details. She visited Dublin's Garden of Remembrance, where the revolutionaries of 1916 are commemorated, laid a wreath, and bowed her head as she did so. To Irish people, especially older ones, it was a moving moment. All their lives they had felt not hated but belittled by England. As the Van Morrison song puts it, "the healing has begun". Small gestures, but possibilities were created.

It's significant that this week's state visit has taken place in the lead-up to Scotland's vote on independence, for, whatever the Scottish electorate decides, a new redefinition of the UK must happen, and soon. Weary of being ruled by the Westminster corruptariat – many of whose members have never even seen Scotland, except on a television screen – Scots are now having versions of exactly the same debates that the Irish had on the verge of independence a century ago: about culture, currency, laws, mores, constitutional and legal arrangements. If Scots decide to leave the UK, or by a small majority to remain, one thing is luminously certain. The 19th century definition of Britain is a work of wish-fulfilment fiction. It doesn't exist anymore, and it hasn't for decades. New stories are about to get written.

England's relationship with its westerly neighbour can be a part of that set of redefinitions. Indeed, it will be, whether we like it or not. The Irish and English are more mixed than they often acknowledge, a fact shown in the telephone directory of any English city, in which thousands of people bearing my own surname and every Irish surname will be found. At Thursday night's concert at the Albert Hall in honour of President Higgins, a remarkable line-up of artists from Glen Hansard and Imelda May to Elvis Costello and Fiona Shaw reflected the Irishness of England.

President Higgins is that rarest of figures in Irish politics, an intellectual who is fuelled by ideas. With a long electoral career as a radical human rights activist in a conservative country, he also inspires a widespread public respect that most politicians can only dream about. His public appearances in Ireland are greeted by standing ovations, at a time when most of his profession would be nervous of entering a room.

The Irish president is constrained by a nexus of constitutional provisos as to what she or he can say. But as was the case with former presidents Mary Robinson and Mary McAleese, it's been clear that a rationalising of Irish-English relationships has been high on President Higgins's agenda. What is "England" anyway, and what is Britain? In one 10-day period recently, the Belfast Telegraph reported seven attacks on Polish immigrants. Indeed, the north of Ireland is currently the most dangerous sector in what is officially the United Kingdom to be a member of an immigrant family. I write as the son of an Ulster Presbyterian who is the least prejudiced person I have ever known, but it sometimes seems that the multicultural and less xenophobic Britain that actually exists isn't the one to which a small minority of Northern Irish loyalists feel loyalty.

And the Republic is undergoing a remaking itself, so radical that it might be characterised as an identity crisis. The once-omnipotent Catholic church has been reduced to deserved irrelevance by the appalling scandal of child sexual abuse. Decades will pass before we've paid for the rampage of the Celtic tiger and the damage left by its prowl. Mass emigration is back. So is rising child poverty. In Ireland we have socialism for the banks, whose every need is supplied while the rest are abandoned to the market.

Yeats wrote that independent Ireland was "no country for old men", but he was tragically wrong on that point. Old men ran the show and made Ireland a reflection of their inadequacies, trading fantasies of an Anglophobic pipe-smoking, cap-doffing theocracy while those they ruled left in multitudes for the land of the foe. Ancient lies don't play so well in Ireland any more. The awakening has been painful, but it's happened. And culture, always the best barometer of any society, has attuned itself to the fragility of borders. Edna O'Brien, John Lydon, Oasis, Elvis Costello, and my sister, Sinead O'Connor, are only some of the artists who display what Morrissey once termed "Irish blood, English heart".

This, for me, is the context of the state visit. It's a piece of public theatre, but so was the Easter Rising in its time, and theatre has its own shimmering importance. David Mamet said the purpose of storytelling is "cleansing awe". The state visit is a kind of catharsis.

As an immigrant to 1980s Britain, as a member by marriage of a London family, as the father of a London-born Irish child, the visit has been moving and meaningful. With all the quaint Gilbert and Sullivan of rite, the speeches and the observances of what are essentially tribal rituals, a truth is being acknowledged. It's a space unearthed by Irish and English people many decades ago now, in culture, intermarriage, sport, business and education, in the work of so many thousands of Irish women in the NHS, and the work of the Irish men who built England. In its own way, it's a homecoming, a telling of the truth.

The state visit is what Philip Larkin, a one-time Ireland resident himself, once described as the trees coming into leaf in spring, "like something almost being said". Many were saying it long ago. Politicians are saying it now. Better late than never.